Representative functions of maximal monotone operators and bifunctions

TL;DR

This paper establishes a connection between representative functions of maximal monotone operators and Fitzpatrick transforms of bifunctions, linking modern and classical theories in monotone operator analysis.

Contribution

It demonstrates that every representative function of a maximal monotone operator can be viewed as a Fitzpatrick transform of a related bifunction, bridging recent and classical theories.

Findings

Shows the equivalence between representative functions and Fitzpatrick transforms.

Links modern theory of representative functions with classical saddle function theory.

Provides a unified framework for understanding maximal monotone operators.

Abstract

The aim of this paper is to show that every representative function of a maximal monotone operator is the Fitzpatrick transform of a bifunction corresponding to the operator. In this way we exhibit the relation between the recent theory of representative functions, and the much older theory of saddle functions initiated by Rockafellar.